Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T09:45:04.788Z Has data issue: false hasContentIssue false
  • English
  • Français

On Simple Rings with Maximal Annihilator Right Ideals

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh
Kwangil Koh*
Affiliation:
N. C. State University at Raleigh Raleigh N. C
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If R is a simple ring with 1 which contains a maximal annihilator right ideal then R is the endomorphism ring of a unital torsion-free module over an integral domain.

We first prove the following:

Let R be a ring with 1. If a ϵ R such that (a)r = {r ϵ R|ar = 0} is a maximal annihilator right ideal then HomR(aR, aR) is an integral domain.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 667 - 668
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Jacobson, N., Structure of Rings, Amer. Math. Soc. Colloquium Publication (1956).Google Scholar